Find the limit as n--> infinity of (1-2/n)^n
We know (1+1/x)^x --> e as n--> infinity
The Attempt at a Solution
I worked it out as e^(-2) using log but I can't get it out using the fundamental limit above. I know it's the square of (1-1/x)^x (where we let x=n/2), just I don't know how to show that (1-1/x)^x --> 1/e. If you could let x |--> -x somehow I'd get the desired result using the limit laws but I'm not sure that's allowed.